Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds?

Meert, Gaëlle; Grégoire, Jacques; Noël, Marie-Pascale

doi:10.1016/j.jecp.2010.04.008

Cited by 105 publications

(110 citation statements)

References 29 publications

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“…In addition, during the subtraction with fractions, students continued to make the same errors and they found the denominator by subtracting the denominators from each other. Also, in similar studies in the Literature, it was concluded that students perceive the numerator and denominator of a fraction as two separate numbers (Biber, Tuna & Aktas, 2013;Haser & Ubuz, 2002;Meert, Grégoire & Noël, 2010;Ni & Zhou, 2005;Pesen, 2008;Soylu & Soylu, 2005;Stafylidou & Vosniadou, 2004).…”

Section: Conclusion and Discussionmentioning

confidence: 90%

“…Because, these misunderstandings not only negatively affect students' learning but also adversely affect their further learning (Baki, 2008). As a result of the literature review, some studieshave been found which analysis the student errors in fractions at all levels of education and the misunderstandings that are the source of these mistakes (Alacaci, 2012;Biber, Tuna & Aktas, 2013;Demiri, 2013;Devika, 2016;Haser & Ubuz, 2002;Jigyel & Afamasaga-Fuata, 2007;Karaagac & Kose, 2015;Kocaoglu & Yenilmez, 2010;Meert, Grégoire & Noël, 2010;Okur & Cakmak-Gurel, 2016;Pesen, 2007;Pesen, 2008;Soylu & Soylu, 2005;Stafylidou & Vosniadou, 2004;Taskın & Yildiz, 2011;Yilmaz & Yenilmez, 2007).…”

Section: Introductionmentioning

confidence: 99%

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Student Errors in Fractions and Possible Causes of These Errors

Aksoy¹,

Yazlık

2017

JETS

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In this study, it was aimed to determine the errors and misunderstandings of 5th and 6th grade middle school students in fractions and operations with fractions. For this purpose, the case study model, which is a qualitative research design, was used in the research. In the study, maximum diversity sampling, which is a purposeful sampling method, was used. For this reason, this study was conducted in a state and a private secondary school on a voluntary basis with 105 5th graders and 84 6th graders, with a total of 189 secondary school students from different levels of achievement. In order to determine students' errors and misconceptions about fractions, two tests were prepared by researchers, ten open-ended questions for 5th graders and twelve open-ended questions for 6th graders. Before these tests were formed, the related field was scanned and the existing misunderstandings were determined. Content analysis method was used on the analyzing of the data. The answer papers of the students were coded and students' solving were examined in three categories as correct, wrong and blank. In addition to this the solving belongs to wrong category was examined in detail and mistakes of the students were coded and the reason of these mistakes were dwelled on. It is seen from the result of the study that students have misunderstanding and mistakes about fractions. It is seen that students are not using the modellings on the operations with fractions because of that most of the mistake and misunderstandings are about operations with fractions.

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Section: Conclusion and Discussionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

Student Errors in Fractions and Possible Causes of These Errors

Aksoy¹,

Yazlık

2017

JETS

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“…Previous behavioral research has mainly focused on the extent to which fractions are represented holistically. This work has focused on the issue of whether the overall (holistic) magnitude of a fraction is accessed automatically, like an integer (Kallai and Tzelgov, 2009;Meert et al, 2010aMeert et al, , 2010bSchneider and Siegler, 2010;Sprute and Temple, 2011). Evidence for holistic magnitude representation come from studies examining the distance effect during fraction comparisons.…”

Section: Representations Of Symbolic Number Typesmentioning

confidence: 99%

Neural representations of magnitude for natural and rational numbers

et al. 2016

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a b s t r a c t a r t i c l e i n f oArticle history: Received 12 January 2016 Accepted 26 July 2016 Available online 26 July 2016 Humans have developed multiple symbolic representations for numbers, including natural numbers (positive integers) as well as rational numbers (both fractions and decimals). Despite a considerable body of behavioral and neuroimaging research, it is currently unknown whether different notations map onto a single, fully abstract, magnitude code, or whether separate representations exist for specific number types (e.g., natural versus rational) or number representations (e.g., base-10 versus fractions). We address this question by comparing brain metabolic response during a magnitude comparison task involving (on different trials) integers, decimals, and fractions. Univariate and multivariate analyses revealed that the strength and pattern of activation for fractions differed systematically, within the intraparietal sulcus, from that of both decimals and integers, while the latter two number representations appeared virtually indistinguishable. These results demonstrate that the two major notations formats for rational numbers, fractions and decimals, evoke distinct neural representations of magnitude, with decimals representations being more closely linked to those of integers than to those of magnitude-equivalent fractions. Our findings thus suggest that number representation (base-10 versus fractions) is an important organizational principle for the neural substrate underlying mathematical cognition.

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“…In cognitive arithmetic (mental calculation of simple equations such as additions and multiplications), this paradigm has been used successfully to demonstrate that the selection of arithmetic facts involves an inhibitory mechanism (Arbuthnott & Campbell, 2000& Campbell, , 2003. The negative priming has been employed also to corroborate inhibition of the selection of the larger denominator when children compare the magnitude of fractions (Meert, Grégoire, & Noël, 2010). In addition, sequential analyses have been performed to demonstrate inhibition in a numerical Stroop task, with reduced congruity effect when the response sequence of the irrelevant dimension is repeated in the task (Cohen Kadosh, Gevers, & Notebaert, 2011).…”

Section: The Current Studymentioning

confidence: 99%

Conflict resolution in two-digit number processing: evidence of an inhibitory mechanism

Macizo

2015

Psychological Research

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We investigated the mechanism involved in conflict resolution when individuals processed two-digit numbers. Participants performed a comparison task in blocks of two trials. In the first trial, between-decade two-digit numbers were used in a compatible condition where the decade and the unit of one number were larger than those of the other number (i.e., 21-73) and an incompatible condition where the decade of one number was larger but the unit was smaller than those of the other number (i.e., 61-53). In the second trial, within-decade two-digit numbers were presented in a related condition where the numbers contained the units presented previously (i.e., 41-43) and an unrelated condition with units that did not appear before (i.e., 48-49). In the first trial, participants responded more slowly in incompatible trials relative to compatible trials. In the second trial, participants were slower in the related condition relative to unrelated trials only after incompatible trials. These results suggest that participants experienced conflict in the incompatible condition of first trial and that they inhibited irrelevant units to resolve conflict.

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Comparing the magnitude of two fractions with common components: Which representations are used by 10- and 12-year-olds?

Cited by 105 publications

References 29 publications

Student Errors in Fractions and Possible Causes of These Errors

Student Errors in Fractions and Possible Causes of These Errors

Neural representations of magnitude for natural and rational numbers

Conflict resolution in two-digit number processing: evidence of an inhibitory mechanism

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